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A323047 Numbers that are not the sum of three (or fewer) 3-smooth numbers.

%I A323047 #34 Jun 11 2019 10:45:21
%S A323047 431,485,509,565,637,671,719,725,727,862,887,935,941,943,959,967,970,
%T A323047 1130,1151,1175,1199,1205,1274,1293,1319,1342,1367,1373,1391,1415,
%U A323047 1421,1423,1438,1439,1445,1447,1450,1453,1454,1455,1481,1527,1535,1559
%N A323047 Numbers that are not the sum of three (or fewer) 3-smooth numbers.
%C A323047 Numbers below 431 may be written as a sum of three (or fewer) elements in A003586. These are the first exceptions.
%C A323047 Below 18431 every number can be written as a sum of 4 or fewer 3-smooth numbers, and below 3448733 every number can be written as a sum of 5 or fewer 3-smooth numbers (cf. sequence A018899).
%H A323047 Robert Israel, <a href="/A323047/b323047.txt">Table of n, a(n) for n = 1..10000</a>
%p A323047 N:= 1000: # for all terms <= N
%p A323047 S:= {seq(seq(2^i*3^j,i=0..ilog2(N/3^j)),j=0..floor(log[3](N)))}:
%p A323047 S2:= select(`<=`,map(t -> op(map(`+`, S,t)), S),N):
%p A323047 S3:= select(`<=`,map(t -> op(map(`+`, S,t)), S2), N):
%p A323047 A:= {$1..N} minus S minus S2 minus S3:
%p A323047 sort(convert(A,list)); # _Robert Israel_, May 19 2019
%t A323047 f[n_] := Union@ Flatten@ Table[2^a * 3^b, {a, 0, Log2[n]}, {b, 0, Log[3, n/2^a]}];
%t A323047 b=Block[{nn = 2000, s}, s = f[nn]; {0, 1, 2}~Join~Select[Union@ Flatten@ Outer[Plus, s, s, s], # <= nn &]]; Complement[Range[2000], b]
%Y A323047 Cf. A003586, A018899, A237442, A323046, A323048, A323049, A323050.
%K A323047 nonn
%O A323047 1,1
%A A323047 _Carlos Alves_, Jan 03 2019